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Effect of random on-site energies on the critical temperature of a lattice Bose gas

  • Physics of Cold Trapped Atoms
  • Published:
Laser Physics

Abstract

We study the effect of random on-site energies on the critical temperature of a non-interacting Bose gas on a lattice. In our derivation the on-site energies are distributed according a Gaussian probability distribution function having vanishing average and variance ν 20 . By using the replicated action obtained by averaging on the disorder, we perform a perturbative expansion for the Green functions of the disordered system. We evaluate the shift of the chemical potential induced by the disorder and we compute, for ν 20 ≪ 1, the critical temperature for condensation. We find that, for large filling, disorder slightly enhances the critical temperature for condensation.

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References

  1. P. W. Anderson, Phys. Rev. 109, 1492 (1958).

    Article  ADS  Google Scholar 

  2. T. V. Ramakrishnan, in Chance and Matter, Ed. by J. Souletie, J. Vannimenus, and R. Stora, Les Houches, Session XLVI (North-Holland, Amsterdam, 1987), p. 213.

    Google Scholar 

  3. C. W. Kiewiet, H. E. Hall, and J. D. Reppy, Phys. Rev. Lett. 35, 1286 (1975).

    Article  ADS  Google Scholar 

  4. J. A. Hertz, L. Fleishman, and P. W. Anderson, Phys. Rev. Lett. 43, 942 (1979).

    Article  ADS  Google Scholar 

  5. M. P. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989).

    Article  ADS  Google Scholar 

  6. K. Huang and H.-F. Meng, Phys. Rev. Lett. 69, 644 (1992)

    Article  ADS  Google Scholar 

  7. S. Giorgini, L. P. Pitaevskii, and S. Stringari, Phys. Rev. B 49, 12938 (1994).

    Google Scholar 

  8. C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Alkali Gases (Cambridge Univ., Cambridge, 2002).

    Google Scholar 

  9. L. P. Pitaveskii and S. Stringari, Bose-Einstein Condensation (Clarendon Press, Oxford, 2003).

    Google Scholar 

  10. J. E. Lye, L. Fallani, M. Modugno, D. S. Wiersma, C. Fort, and M. Inguscio, Phys. Rev. Lett. 95, 070401 (2005).

    Google Scholar 

  11. D. Clement, A. F. Varon, M. Hugbart, J. A. Retter, P. Bouyer, L. Sanchez-Palencia, D. M. Gangardt, G. V. Shlyapnikov, and A. Aspect, Phys. Rev. Lett. 95, 170409 (2005).

    Google Scholar 

  12. L. Fallani, J. E. Lye, V. Guarrera, C. Fort, and M. Inguscio, Phys. Rev. Lett. 98, 130404 (2007).

    Google Scholar 

  13. G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).

    Article  ADS  Google Scholar 

  14. J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).

    Article  ADS  Google Scholar 

  15. O. Morsch and M. Oberthaler, Rev. Mod. Phys. 78, 179 (2006).

    Article  ADS  Google Scholar 

  16. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).

    Article  ADS  Google Scholar 

  17. T. Giamarchi and H. J. Schulz, Phys. Rev. B 37, 325 (1988).

    Article  ADS  Google Scholar 

  18. H. Gimperlein, S. Wessel, J. Schmiedmayer, and L. Santos, Phys. Rev. Lett. 95, 170401 (2005).

    Google Scholar 

  19. A. M. Rey, I. I. Satija, and C. W. Clark, Phys. Rev. A 73, 063610 (2006).

    Google Scholar 

  20. K. V. Krutitsky, A. Pelster, and R. Graham, New J. Phys. 8, 187 (2006).

    Article  ADS  Google Scholar 

  21. T. Roscilde and J. I. Cirac, Phys. Rev. Lett. 98, 190402 (2007).

    Google Scholar 

  22. P. Sengupta and S. Haas, Phys. Rev. Lett. 99, 050403 (2007).

    Google Scholar 

  23. P. Buonsante, V. Penna, A. Vezzani, and P. B. Blakie, Phys. Rev. A 76, 011602 (2007).

    Google Scholar 

  24. T. Roscilde, Phys. Rev. A 77, 063605 (2008).

    Google Scholar 

  25. X. Deng, R. Citro, A. Minguzzi, and E. Orignac, Phys. Rev. A 78, 013625 (2008).

    Google Scholar 

  26. G. Roux, T. Barthel, I. P. McCulloch, C. Kollath, U. Schollwöck, and T. Giamarchi, Phys. Rev. A 78, 023628 (2008).

    Google Scholar 

  27. S. Morrison, A. Kantian, A. J. Daley, H. G. Katzgraber, M. Lewenstein, H. P. Buchler, and P. Zoller, New J. Phys. 10, 073032 (2008).

    Google Scholar 

  28. K. V. Krutitsky, M. Thorwart, R. Egger, and R. Graham, Phys. Rev. A 77, 053609 (2008).

    Google Scholar 

  29. U. Bissbort and W. Hofstetter, arXiv:0804.0007.

  30. G. Roati, M. Zaccanti, C. D’Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, Phys. Rev. Lett. 99, 010403 (2007).

    Google Scholar 

  31. L. Dell’Anna, S. Fantoni, P. Sodano, and A. Trombettoni, J. Stat. Mech. P11012 (2008).

  32. A. V. Lopatin and V. M. Vinokur, Phys. Rev. Lett. 88, 235503 (2002).

    Google Scholar 

  33. O. Zobay, Phys. Rev. A 73, 023616 (2006).

    Google Scholar 

  34. M. Timmer, A. Pelster, and R. Graham, Europhys. Lett. 76, 760 (2006).

    Article  ADS  Google Scholar 

  35. G. M. Falco, A. Pelster, and R. Graham, Phys. Rev. A 75, 063619 (2007).

    Google Scholar 

  36. V. I. Yukalov and R. Graham, Phys. Rev. A 75, 023619 (2007).

    Google Scholar 

  37. V. I. Yukalov, E. P. Yukalova, K. V. Krutitsky, and R. Graham, Phys. Rev. A 76, 053623 (2007).

    Google Scholar 

  38. D. C. Mattis, The Theory of Magnetism II (Springer, Berlin, 1985).

    Google Scholar 

  39. L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981).

    MATH  Google Scholar 

  40. C. De Dominicis and I. Giardina, Random Fields and Spin Glasses: A Field Theory Approach (Cambridge Univ., Cambridge, 2006).

    MATH  Google Scholar 

  41. G. S. Joyce, J. Phys. A 5, L65 (1972).

    Article  ADS  Google Scholar 

  42. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Ed. by M. Abramowitz and I. A. Stegun (National Bureau of Standards, Washington, DC, 1964).

    MATH  Google Scholar 

  43. J.-P. Blaizot, arXiv:0801.0009.

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Authors and Affiliations

  1. International School for Advanced Studies, Via Beirut 2/4, 1-34014, Trieste, Italy

    L. Dell’Anna, S. Fantoni & A. Trombettoni

  2. INFN, Sezione di Trieste, Trieste, Italy

    S. Fantoni & A. Trombettoni

  3. INFM, CNR-DEMOCRITOS National Supercomputing Center, Trieste, Italy

    S. Fantoni

  4. Dipartimento di Fisica and INFN, Sezione di Perugia, Università di Perugia, Via A. Pascoli, I-06123, Perugia, Italy

    P. Sodano

Authors
  1. L. Dell’Anna
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  2. S. Fantoni
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  3. P. Sodano
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  4. A. Trombettoni
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Corresponding author

Correspondence to A. Trombettoni.

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Original Text © Astro, Ltd., 2009.

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Dell’Anna, L., Fantoni, S., Sodano, P. et al. Effect of random on-site energies on the critical temperature of a lattice Bose gas. Laser Phys. 19, 571–577 (2009). https://doi.org/10.1134/S1054660X09040069

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  • DOI: https://doi.org/10.1134/S1054660X09040069

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